equal perimeters or bounds (whence the name is de- 
rived), but whatever relates to the Maxima and Mi- 
nima of quantities depending on a line, fpace, or 
body, whereof the figure is unknown, is, by ma- 
thematicians, included under that denomination. 
But notwithftanding the ufefulnefs and great ex- 
tent of this fiibjeft, nothing (that I know of) had 
been done thereon farther than the refolution of cer- 
tain particular cafes (fuch as finding the line of the 
fwifteft defeent, and the folid of the leafi; refiftance), 
’till the celebrated mathematician M' Laurin, in his 
treatife of fluxions, gave the invefHgation of an ele- 
gant and very eafy method, whereby the principal 
problems belonging to the firfl; order may be re- 
folved. 
The paper ,I have now the honour to lay before 
the Society contains farther improvements on this 
fubjed:: as it is by far more general than any thing 
yet offered^ and is drawn up with a view to obviate 
the difficulties attending the refolution of a very in- 
tricate kind of problems, and thereby to open an 
eafy way to fome very interefting inquiries in natu- . 
ral philofophy, I cannot doubt of its meeting with a 
favourable reception. 
Lemma I. 
Fig. I. At any given points 2), G, 7, Z, in a right- 
line A Ly fuppofe perpendiculars to be ereded ; 
and from any other given points r,/', 2, 2, at equal 
diflances [c D\ fG\ hT, klJy) from the faid 
perpendiculars, refpedively, conceive right-lines 
c dyfgy h iy kly to be drawn, to terminate fome- 
where in the faid perpendiculars j let ^ A, »S, 7^ 
denote.' 
